# @Time : 2021/8/4 14:26
# @Author : Li Kunlun
# @Description : 多项式函数拟合实验
import utils as d2l
from mxnet import autograd, gluon, nd
from mxnet.gluon import data as gdata, loss as gloss, nn
from matplotlib import pyplot as plt

# 1、生成数据集
"""
1、使用如下的三阶多项式函数来生成该样本标签：
    y = 1.2 * x -3.4 * x^2 + 5.6 * x^3 +5 +theta(N(0,0.1)) 
"""
n_train, n_test, true_w, true_b = 100, 100, [1.2, -3.4, 5.6], 5
features = nd.random.normal(shape=(n_train + n_test, 1))
poly_features = nd.concat(features, nd.power(features, 2), nd.power(features, 3))
labels = (true_w[0] * poly_features[:, 0] + true_w[1] * poly_features[:, 1] + true_w[2] * poly_features[:, 2] + true_b)
labels += nd.random.normal(scale=0.1, shape=labels.shape)


# 2、定义、训练和测试模型
# 定义作图函数semilogy，其中 𝑦 轴使用了对数尺度
def semilogy(x_vals, y_vals, x_label, y_label, x2_vals=None, y2_vals=None, legend=None, figsize=(3.5, 2.5)):
    d2l.set_figsize(figsize)
    d2l.plt.xlabel(x_label)
    d2l.plt.ylabel(y_label)
    d2l.plt.semilogy(x_vals, y_vals)
    if x2_vals and y2_vals:
        d2l.plt.semilogy(x2_vals, y2_vals, linestyle=':')
        d2l.plt.legend(legend)
    plt.show()


num_epochs, loss = 100, gloss.L2Loss()


def fit_and_plot(train_features, test_features, train_labels, test_labels):
    net = nn.Sequential()
    net.add(nn.Dense(1))
    net.initialize()
    batch_size = min(10, train_labels.shape[0])
    train_iter = gdata.DataLoader(gdata.ArrayDataset(train_features, train_labels), batch_size, shuffle=True)
    trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.01})
    train_ls, test_ls = [], []
    for _ in range(num_epochs):
        for X, y in train_iter:
            with autograd.record():
                l = loss(net(X), y)
            l.backward()
            trainer.step(batch_size)
        train_ls.append(loss(net(train_features), train_labels).mean().asscalar())
        test_ls.append(loss(net(test_features), test_labels).mean().asscalar())
    print('final epoch: train loss', train_ls[-1], 'test loss', test_ls[-1])
    semilogy(range(1, num_epochs + 1), train_ls, 'epochs', 'loss', range(1, num_epochs + 1), test_ls, ['train', 'test'])
    print('weight:', net[0].weight.data().asnumpy(), '\nbias:', net[0].bias.data().asnumpy())


# 3、三阶多项式函数拟合（正常）
"""
final epoch: train loss 0.00699347 test loss 0.00635088
weight: [[ 1.17456579 -3.3916204   5.60125017]] 
bias: [ 4.98684025]
"""
fit_and_plot(poly_features[:n_train, :], poly_features[n_train:, :], labels[:n_train], labels[n_train:])

# 4、线性函数拟合（欠拟合）
"""
final epoch: train loss 159.335 test loss 103.298
weight: [[ 22.71021461]] 
bias: [-0.6747697]
"""
fit_and_plot(features[:n_train, :], features[n_train:, :], labels[:n_train], labels[n_train:])

# 5、过拟合 - 使用两个样本进行训练，导致过拟合
"""
final epoch: train loss 0.475768 test loss 133.275
weight: [[ 2.05884576  1.92736685  2.04774022]] 
bias: [ 2.4821291]
"""
fit_and_plot(poly_features[0:2, :], poly_features[n_train:, :], labels[0:2], labels[n_train:])
